问题 问答题

驾驶证考试中的路考,在即将结束时要进行目标停车,考官会在离停车点不远的地方发出指令,要求将车停在指定的标志杆附近,终点附近的道路是平直的,依次有编号为A、B、C、D、E的5根标志杆,相邻杆之间的距离△L=12.0m.一次路考中,学员甲驾驶汽车,学员乙坐在后排观察并记录时间,学员乙与车前端面的距离为s=2.0m.假设在考官发出目标停车的指令前,汽车是匀速运动的,当学员乙经过O点考官发出指令:“在D标志杆目标停车”,发出指令后,学员乙立即开始计时,学员甲需要经历△t=0.5s的反应时间才开始刹车,幵始刹车后汽车做匀减速直线运动,直到停止.学员乙记录下自己经过B、C杆时的时刻tB=4.5s、tC=6.50s.己知LOA=44m.求:

(1)刹车前汽车做匀速运动的速度大小W及汽车开始刹车后做匀减速直线运动的加速度大小a;

(2)汽车停止运动时车头前端面离D的距离.

答案

(1)汽车从O到标志杆B的过程中:

LOA+△L=v0△t+v0(tB-△t)-

1
2
a(tB-△t)2

汽车从O到标志杆C的过程中:

LOA+2△L=v0△t+v0(tC-△t)-

1
2
a(tC-△t)2

联立方程组得:

v0=16m/s

a=2m/s2

(2)汽车从开始到停下运动的距离:

x=v0△t+

v02
2a

可得x=72m

因此汽车停止运动时车头前端面在CD之间离D

LOA+3△L-s-x=44+36-2-72=6m.

答:(1)刹车前汽车做匀速运动的速度大小为16m/s,

汽车开始刹车后做匀减速直线运动的加速度大小a为2m/s2

(2)汽车停止运动时车头前端面离D的距离为6m.

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